Question

HELP PLEASE

Answer 1

The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy or New York, New York:

Maximum Minimum Q1 Q3 IQR Median Mean σ
Rome 16 0 3 13 10 8.5 8 5.4
New York 20 1 4.5 6 1.5 5.5 7.25 6.1

Which of the choices below best describes how to measure the center of this data?
Both centers are best described with the mean.
Both centers are best described with the median.
The Rome data center is best described by the mean. The New York data center is best described by the median.
The Rome data center is best described by the median. The New York data center is best described by the mean.

Answer 2

@mathmate

Answer 3

@confluxepic

Answer 4

I think the problem with this question is the word "centre", which is not mathematically defined. Both mean and median measure central tendencies, and each is a better measure under different conditions.
Since "centre" is not mathematically defined, I will give a subjective recommendation.
In the first case (Rome), both number should be an adequate measure, since they are both centrally located within the data, especially between Q1 and Q3.
I would prefer 8 since it is smack centred between Q1 and Q3, while 8.5 is a little off.
For the second case (NY), the mean is 7.5 which is higher than Q3 of 6. This is typically the case when most would prefer to use the median (5.5) where there is an equal number of data above and below (5.5). The reason for the mean to be shifted to 7.5 means there are more data closer to the maximum (20) than there are to the minimum (1), or data are skewed.

Answer 5

a then @mathmate @mathstudent55 can you make sure i said this correctly

Answer 6

If you read my response carefully, you'll find that MY answer is not a. However, as I said, it is a subjective answer, so I am open to any answer. If you prefer a, perhaps you would share with us why so.

Answer 7

becsue if you look the mean seems the most knowledgeable answer and make sense

Answer 8

and both centers are best described with mean @mathmate

Answer 9

@iGreen

Answer 10

Both mean and median are each some measure of the centre of the data. We are required to find the "centre" which does not have a statistical definition (unless of course if i am mistaken). So the answer would be as vague as the question. I have a preference which I mentioned above, but cannot guarantee it was what was expected.
Just in case you have a confusion with the numbers presented in a convoluted way, can you complete the table below?